The fact is, I question anyone can tell you how many amps the blower pulls overnight. Far too many variables. To add more batteries may not be the answer, simply due to the fact you have to charge them every day.
In my opinion and experience, adding a Wave3 (or equal) will solve the problem. The Wave3 requires no battery, uses propane only. It can be installed as a portable or permanent. It is a CAT heater, not to be confused with non-CAT heaters.
I realize your original post inquired about batteries/furnace, but the Wave3 lightens the load of both.
Wayne